On the computation of parameter derivatives of solutions of linear difference equations

AbstractA method is given to compute the parameter derivatives of recessive solutions of second-order inhomogeneous linear difference equations. The case of difference equations in which all solutions have the same rate of growth is also discussed.The method is illustrated by numerical computations of parameter derivatives of incomplete gamma functions and confluent hypergeometric functions

Asymptotic expansions for qq-gamma, qq-exponential, and qq-Bessel functions

AbstractNew asymptotic expansions are given for the q-gamma function, the q-exponential functions, and for the Hahn-Exton q-Bessel function. For the theta functions, four expansions are given. And for the Hahn-Exton q-Bessel difference equation, a new solution is given, which forms with the Hahn-Exton q-Bessel function a numerically satisfactory pair of solutions

Hyperasymptotics and hyperterminants: Exceptional cases

AbstractA new method is introduced for the computation of hyperterminants. It is based on recurrence relations, and can also be used to compute the parameter derivatives of the hyperterminants. These parameter derivatives are needed in hyperasymptotic expansions in exceptional cases. Numerical illustrations and an application are included

Uniform asymptotic approximation of Fermi—Dirac integrals

AbstractThe Fermi–Dirac integral Fq(x)=1Γ(q+1)∫0∞tq1+et−xdt, q>−1, is considered for large positive values of x and q. The results are obtained from a contour integral in the complex plane. The approximation contains a finite sum of simple terms, an incomplete gamma function and an infinite asymptotic series. As follows from earlier results, the incomplete gamma function can be approximated in terms of an error function